## Gravity as Separational Insufficiency

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### Gravity as Separational Insufficiency

Below I address questions relating to my article "A Simple Spin on Gravity" which is admittedly fast paced as it builds on two brief prior articles, ALPHA: Applying a Light Touch? and Spin½ 'Plane' & Simple. Associated animations (avg. 6 min.) are found here.

I'll start here with first principles. These are a set of foundational assumptions upon which any model rests. Occam's razor prefers simplicity. "Phyxed" (physics-fixed, better than real) is the model I use to solve many mysteries of the Standard Model, including gravity.

"The Standard Model of particle physics is the theory describing three of the four known fundamental forces (the electromagnetic, weak, and strong interactions, and not including the gravitational force)…"

Phyxed derives the standard model from just 3 first principles to which I'll refer.
Details follow (to facilitate post-specific replies).

Exceedingly Simple First Principles:
1. One kind of dimension:
2. One kind of object:
3. One kind of behavior:

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### Re: Outward Bound

1. One kind of dimension: Physics uses the same term "dimension" for two different things, space and time. Space offers back and forth (bidirectional) translational freedom in each of three dimensions. Time offers forward-only (unidirectional) translational freedom in one dimension. Aging is observed at different rates, but even non-aging light can't travel backward in time.

Space is depicted as a line with arrows at both ends. Time is shown as a ray with an arrow extending away from an origin. Our continuum fundamentally provides 4D of potential separation, allowing 4D "events" to be different. Thus, four coordinates are needed to distinguish one event from another. Both space and time offer equivalent separation but typically in different, proportional units.

Phyxed models all four dimensions as temporal. With origins collected at a single point a radial temporal 4-field arises from what would be the singularity of the Big Bang. Since a 4-ball is enclosed by a 3-sphere, that 3-sphere constitutes the 3D "space" of the cosmos, expanding as it ages.

An n-dimensional ball is enclosed by an (n-1)-dimensional sphere.

Like known electric and magnetic fields but one dimension up, a radial temporal 4-field originates at a point and is unidirectional. The enclosing cosmos expands with age.

Rather than entropy giving time its arrow, it is unidirectional time which drives entropy. The expanding cosmos provides space for an ever-increasing number of random states (particle arrangements) compared to those which are ordered.

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2. One kind of object: The simplest object possible in a continuum is a discontinuity: a hole. It is the object from which all others in the cosmos arise. Informationally, it is a fundamental bit. Holes have no internal span (if they do they are "tubes"). Like hole in a piece of paper, a hole connects what's on one side with what's on the other. By convention, the dimension of a hole is given by the dimension of its enclosure. For a circular hole, the circumference is made from a 1D line, so that whole is considered a 1-hole. A massive black hole is enclosed by a 2-sphere (event horizon) so it's a 2-hole. A hole can have direction, which can, in principle, change by rotation about a hole's diameter.

"the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is "not there", it is not immediately obvious how to define a hole or how to distinguish different types of hole.."

Phyxed asserts a "pinhole" (particle-interaction wormhole), a hole with a lightlike direction. It is thus, a speed c-dependent hole, accessible only to energy. In Special Relativity (SR), a lightlike trajectory has a slope of 1 in natural units. Lightlike intervals have magnitude zero, i.e. zero interval separation or "interval contact". So, a pinhole is a hole which acts as an energy conduit through space & time.

Though a lightlike "worldline" appears to have length in spacetime diagrams, its zero magnitude implies that events A, B, C, & D are co-located, the same spacetime event with different coordinates. This is not uncommon on Euclidean maps of non-Euclidean geometry. A Mercader projection of the south pole similarly appears to have length, where A, B, C, & D are a single geographic location with different longitudinal coordinates. As shown, the south pole and a pinhole are both examples of projected contact.

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### Re: On Best Behavior

3. One kind of behavior: The simplest of all behaviors is spin, from which all other behaviors may arise. It can represent motion without translation, spinning at a single spatial location, or with translation seen as rolling. All particles in the Standard Model have a property of "intrinsic spin" which has real, conserved units of angular momentum but for which a primary axis has never been identified. (see my Spin½ Plane & Simple).

Phyxed models intrinsic spin as "chronaxial", having a temporal primary spin axis. Such spin would then occur in a 3-plane as solid-angular spin. Time is never in the plane of rotation because unidirectionality prohibits the needed oscillatory freedom. But if time is robust enough to support translation (i.e. everything goes to the future), it can also serve as an axis of rotation.

Phyxed models curved-space, radial-time (see First Principle 1), where radial time is normal to space at all locations and the plane of rotation is an interval 3-plane. By definition, a spin vector has no projection on its plane of rotation. But on a spatial sphere chronaxial spin casts equal magnitude projections in every direction (half measured as negative), exactly as observed.
Chronaxial spin has projections on curved space in every direction.

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phyti » May 13th, 2020, 2:05 pm wrote:If Einstein's invariant interval were rotated about its center in all directions, the ends would trace out a sphere. It's invariant since it doesn't change over time, events don't move. Thus no need of a 'time' coordinate, which is assigned by each observer according to their local clock, essentially for id purposes.
An event has no property labeled 'time'. If I eat lunch at the same place 5 days in a row, each lunch needs an identifier to distinguish it from the others. My cell phone assists me with a calendar.

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### Travel Light, Go Far

Pinhole + Chronaxial Spin = Gravity

phyti wrote:If Einstein's invariant interval were rotated about its center in all directions, the ends would trace out a sphere.
Yes! Rims of a so-called light "cone" are such spheres. For clarity, it's often worth appending the dimension to an object. For example, the rim of a light cone can equivalently be called a "2-circle" or a "2-sphere", which are both the same as an ordinary sphere: the set of points equidistant from a central location in 3D.

Light cone rims are actually spheres. The light "cone" is really a "3-cone" and a plane which cuts across any of its sections is a "3-plane".

phyti wrote:It's invariant since it doesn't change over time, events don't move.
"Invariance" does not usually refer to an interval being fixed. It refers to the fact that its magnitude (4D span) is the same to all inertial observers, though observers in different inertial frames will ascribe different spatial and temporal components to an interval.

Worldlines of ordinary objects are fixed in spacetime but we can imagine them moving. And there is no way to deny chronaxial spin of a null worldline (one having zero interval span) as is the case for those which are lightlike (my pinholes).

phyti wrote:Thus no need of a 'time' coordinate…
Fair point! A spin vector is an abstraction along a real or imagined axis, normal to the plane of rotation. Thus, a Flatlander has no need of an actual 3rd dimensional axis to rotate or orbit within its plane of existence.

What would you say however, about a hole in Flatland itself? What would it connect? A hole is meaningless unless it is from somewhere to somewhere. Thus, I fall back on the first principles of Phyxed.
1. Time comprises all dimensions as a radial 4-field emanating from the big Bang.
2. The one fundamental kind of object is a pinhole. It is a hole in a spatial simultaneity connecting a prior event to a later one. I'm not saying you have to believe this is "real" just that it is the model Phyxed. Because this model is the simplest possible, it will take you further than any other, in terms of explanatory power.

phyti wrote:An event has no property labeled 'time'
An event is a location in spacetime, which is identified by 3 spatial and one temporal coordinates. Their values depend on the coordinates specific to each inertial frame. I'm fine with not calling a relative label a property. But we do need four identifiers to distinguish one event from another. Even in a particular inertial frame, a single event can have more than one coordinate identity. Such co-located identities are "separated" by zero intervals. I'm asserting that every event on a light cone is the same event. Jorrie will be debating that with me in another thread.

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### Re: Gravity as Separational Insufficiency

phyti » May 15th, 2020, 1:05 pm wrote:Read the paper a few times, see new concepts but don't understand what sustains them, source of energy, etc. How or why does a pinhole form? Is the 'rope' an extension of 'string theory'? Einstein already dealt with gravity as a field and mass as its energy source. True, the process needs elaboration, so why not work on that. Maybe space has a structure yet to be discovered, supporting Einstein's ether.
Overall the contents seem to be overly complicated.

Here is what can be extracted from existing SR theory.
On the left, a typical spacetime graphic, with the U-frame as a reference, observing anaut A in motion in direction x. A sends a light signal (blue) that reflects from the end of a stick (event R) and returns to A (event D). A assigns time of R as h, half of light transit time, per SR convention.
In 4D, things are moving in spacetime, the area contained by the Ut and Ux axes.

The spacetime graphic is very useful in simplifying cases to the essential elements and showing multiple relations visually, as in the 'picture is worth many words' adage.
My objections are the use of metaphorical interpretations, moving in time, 4-vectors, infinite mass, etc., as if they are the reality, when they are just the methods of analysis.

https://app.box.com/s/o1qpkjkt7ilklnz63no6itt9s0ceui1j

In reality, A and the light are moving as shown by the arrows at the bottom.
The red line indicates t', the time indicated on the A-clock. In transferring the interval t' to the At line or 'time line', the units would be expanded (dilated), as typically shown with tick marks. This means A and the A-clock are moving in one spatial dimension, in the x direction, leaving a 2D plane perpendicular to x, as shown on the right. The clock is generating its own local time (there is no universal time), so 'time' doesn't need a dimension.

https://app.box.com/s/somn42vezm5057knmpkdhv2hw22dku3t

Then there is perception space, represented in the light cone graphic, with observer U at the apex, which technically would be a small circle. For U the present is a brief interval of a few milliseconds of mental processing of sensory input. The 2D plane, with an object e in motion in the x direction, is projected onto the light cone, representing a history of e over time. Object e approaches from a distance, passes U with a minimum separation of d, then recedes to an increasing distance. The images of e require more light transit time to either side of P, the direction perpendicular to x. For U, the past is synonymous with distance, and e could move in the reverse direction. There is no future light cone since U can't have awareness of events that haven't happened.
Note the path of e is a hyperbola on the cone, and the only instance of distance varying in a linear mode is on the x axis. The typical case would be a hyperbola with hyperbolic time values. This was the case before SR.

https://app.box.com/s/52oddzqn3agfsgpxln5548rbx262qdmn

In addition to the t&x axes folding scissors style, the perceived world of the near light speed observer shrinks toward a limit of zero.

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phyti wrote:…don't understand what sustains them, source of energy…
In Phyxed energy is precisely the chronaxial spin rate (excluding dark matter and dark energy to be addressed later.) Higher spin rate creates more instances of a gravitational field per unit time. Thus, energy and gravitational mass are inexorably linked. Think of each field instance as a light cone because gravity (as with all force) is lightlike. More cones on the timeline is higher gravity.

phyti wrote:How or why does a pinhole form?
Pinholes are the fundamental object of First Principle 2. It is a hole in our continuum pointing in a lightlike direction. It is the object from which all others arise, most notably by spinning to produce a field. Consider a pinhole as a "force object" which by spinning instantaneously about time creates a field of potential force (e.g. on a test particle).

phyti wrote:Is the 'rope' an extension of 'string theory'?
No, string theory needs far too many dimensions (most often 11) of inexplicably different types. I just meant an ordinary rope. Spin it fast and you create a field where average density falls off with radius. Of course, that's in an ordinary 2-plane of rotation.

If you could spin it around time, the density field would follow the inverse square law. What a coincidence! Almost too simple. Phyxed identifies mysterious intrinsic spin as chronaxial and it just so happens that it naturally provides the inverse square law for resulting fields. Every massive particle has them.

phyti wrote:Einstein … gravity as a field and mass as its energy source. True, the process needs elaboration, so why not work on that.
That's what Phyxed does. A pinhole is projected contact. Contact is the opposite of separation. Spinning the projection around time creates a field following the inverse square law where the separational capacity of the continuum is compromised. Things in the field can no longer maintain their separation from its source. That's all there is to it!

phyti wrote:Maybe space has a structure yet to be discovered
We don’t have to change the structure of space or even curve it. Instead we use a structural element, specifically a pinhole as a radial field element (like a rope) and give it chronaxial spin.

phyti wrote:Overall the contents seem to be overly complicated.
That may be because the article builds on two previous articles on pinholes and spin. The bottom line is exceedingly simple:
Gravity = Pinhole + Chronaxial Spin

phyti wrote:My objections are the use of metaphorical interpretations, moving in time
Chronaxial spin is most objectionable because it is instantaneous. Think about it. Any motion around a time axis takes no ∆t to accomplish. That would violate speed limit c! Except for two things: 1. a pinhole has no length so there is no circumferential speed. 2. a pinhole is a projection of contact and projections are exempt from speed limit c. (see Faster than light)

phyti wrote:there is no universal time
We do have a 'universal' time reference in the age of the cosmos. Aging is fastest in a rest frame, the cosmos can't move relative to itself, so it has always been in its rest frame. Nothing in the cosmos is older than the cosmos. The age of the cosmos can serve as a common maximally aged reference to all its inhabitants.

Aside from that, Phyxed employs time as the only kind of dimension in first principle 1. All four dimensions are filled by a radial temporal 4-field.

phyti wrote:There is no future light cone since U can't have awareness of events that haven't happened.
then we're not talking about SR which uses light cones to determine regions of causality. Phyxed strives to be compatible with SR. though photons are replaced by pinhole contact, the particle aspect of light (e.g. photoelectric effect) is perfectly maintained. A light cone is seen as the result of spinning a pinhole. It is an instance of a field.

A pinhole as a lightlike radial field element generates a field when rotated about time

phyti wrote: n addition to the t&x axes folding scissors style, the perceived world of the near light speed observer shrinks toward a limit of zero.
Agreed. So does the interval separation between emitter and absorber. But for a light quantum it's not an asymptote, its actually zero interval separation (interval contact).